1204.0395 (El Hassan Saidi)

Mutation Symmetries in BPS Quiver Theories: Building the BPS Spectra    [PDF]

El Hassan Saidi

We study the basic features of BPS quiver mutations in 4D $\mathcal{N}=2$ supersymmetric quantum field theory with $G=ADE$ gauge symmetries. We show, for these gauge symmetries, that the set of quiver mutations form a discrete group $\mathcal{G}_{Mut}^{G}$ capturing all information about the BPS spectra. In the strong coupling limit, it is shown that the corresponding discrete groups $\mathcal{G}_{strong}^{G}$ are isomorphic to the discrete dihedral groups $Dih_{2h_{G}}$ contained in Coxeter(G) with $h_{G}$ the Coxeter number of G. These discrete groups allow to determine the BPS spectrum of the strong coupling chamber; and give another way to count the total number of BPS and anti-BPS states of $\mathcal{N}=2$ gauge theories. We also build the matrix realization of these mutation groups $% \mathcal{G}_{strong}^{G}$ from which we read directly the electric-magnetic charges of the BPS and anti-BPS states of $\mathcal{N}=2$ QFT$_{4}$ as well as their matrix intersections. We study as well the quiver mutation symmetries in the weak coupling limit and give their links with infinite Coxeter groups. We show amongst others that $\mathcal{G}_{weak}^{su_{2}}$ is contained in ${GL}({2,}\mathbb{Z}) $; and isomorphic to the infinite Coxeter ${I_{2}^{\infty}}$. Other issues such as building $\mathcal{G}_{weak}^{so_{4}}$ and $\mathcal{G}_{weak}^{su_{3}}$ are also studied.} \keywords{Electric magnetic duality in $\mathcal{N}=2$ QFT$_{4}$, BPS quiver theory, Quiver mutations, Building BPS spectra

View original: http://arxiv.org/abs/1204.0395